Problem: Let $f(x) = -9x^{2}-2x+5$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-9x^{2}-2x+5 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -9, b = -2, c = 5$ $ x = \dfrac{+ 2 \pm \sqrt{(-2)^{2} - 4 \cdot -9 \cdot 5}}{2 \cdot -9}$ $ x = \dfrac{2 \pm \sqrt{184}}{-18}$ $ x = \dfrac{2 \pm 2\sqrt{46}}{-18}$ $x =\dfrac{1 \pm \sqrt{46}}{-9}$